Prices of anarchy, information, and cooperation in differential games

Tamer Başar, Quanyan Zhu

Research output: Contribution to journalArticlepeer-review


The price of anarchy (PoA) has been widely used in static games to quantify the loss of efficiency due to noncooperation. Here, we extend this concept to a general differential games framework. In addition, we introduce the price of information (PoI) to characterize comparative game performances under different information structures, as well as the price of cooperation to capture the extent of benefit or loss a player accrues as a result of altruistic behavior.We further characterize PoA and PoI for a class of scalar linear quadratic differential games under open-loop and closed-loop feedback information structures. We also obtain some explicit bounds on these indices in a large population regime.

Original languageEnglish (US)
Pages (from-to)50-73
Number of pages24
JournalDynamic Games and Applications
Issue number1
StatePublished - Mar 2011


  • Differential games
  • Efficiency
  • Information structures
  • Linear-quadratic games
  • Nash equilibria
  • Price of anarchy
  • Price of cooperation
  • Price of information

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Economics and Econometrics
  • Statistics and Probability
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design


Dive into the research topics of 'Prices of anarchy, information, and cooperation in differential games'. Together they form a unique fingerprint.

Cite this